A method for acquiring a 3D image dataset for an image object. results from a generalization of an article by Y. Censor, T. Elfving, G. T. Herman: “A Method of Iterative Data Refinement and its Applications”, Math. Meth. Appl. Sci. 7 (1985), pages 108-123.
The application deals in particular with x-ray imaging. In each instance a 2D image dataset is acquired with the aid of an x-ray radiation source and an x-ray radiation detector. These are moved into different positions, with a coupled movement of the x-ray radiation source and the x-ray radiation detector taking place. Such a 2D image dataset is acquired in each position, in that the x-ray radiation source emits x-ray radiation, the x-ray radiation is attenuated by the image object, being attenuated to different degrees by different regions of the image object, with the degree of attenuation by the respective regions of the image object showing up as gray scale values, which are acquired with the aid of the x-ray radiation detector. These 2D image datasets can also be referred to as “projection images”. If a sufficiently large number of projection images are acquired in suitable positions, a mathematical method can be used to reconstruct a 3D image dataset. A 3D image dataset indicates for volume elements in the space taken up by the image object the degree to which the image object attenuates the x-ray radiation in the region of the volume element. Gray scale values are thus assigned to 3D volume elements.
The problem regularly arises of configuring the so-called back projection, in other words the mapping of the 2D image datasets onto the 3D image dataset, as optimally as possible so that the 3D image dataset reproduces the actual properties of the image object as far as possible. The mathematical method can be reproduced by an operator B for the 3D reconstruction. In the simplest instance said operator can simply be applied to data from the 2D image datasets. The 2D image datasets are described appropriately as vector g here.
However properties are also now known of the mapping of the three-dimensional space, in which the image object is located, onto the respective plane of the x-ray radiation detector, which is typically a flat screen x-ray detector. It is thus possible to a certain extent, by applying an operator A describing a projection image acquisition, to verify whether the original vector g of the 2D image datasets (the projection images) ultimately results again. According to the article by Y. Censor et al. cited in the introduction, the result of the application of the operator A describing the projection image acquisition to the result of the application of the operator B to the vector g, ABg, can also be part of a correction of the data values acquired for the 3D image dataset. In this process an auxiliary dataset is defined (appropriately in the form of a vector) and, typically after initialization of the auxiliary dataset, in each iteration the operator B for the 3D reconstruction is applied to the auxiliary dataset and the auxiliary dataset is then corrected based on an operator A applied to said provisional 3D image dataset acquired in this manner and describing the image acquisition and based on the 2D image datasets g. If we refer to the auxiliary dataset as φ and set the provisional result for the 3D image dataset to ƒ(i)=Bφ(i), it is proposed that φ(i+1) be calculated usingφ(i+1)=φ(i)+λ(i)(g−Aƒ(i)),  (1)where λ(i) is a factor that can be the same for every iteration or can be different for different iterations. If the correct reconstruction operator B=A−1 is now found exactly, no iteration would be required. However the 3D reconstruction typically includes simplifying assumptions and brings about artifacts resulting from such assumptions, so that with appropriate selection of the prefactors λ(i) an initially gradual convergence takes place in the method, so that at some point (g−A ƒ(i)) becomes smaller than ε, where ε is a suitable limit value.
During imaging with x-ray radiation there is inevitably scattered radiation. Scattered radiation is radiation which does not penetrate the image object in a straight line.
For example it is known from the article by M. Zellerhoff, B. Scholz, E.-P. Rührnschopf, B. Brunner: “Low contrast 3D reconstruction from C-arm data”, Proceedings of SPIE Conference 2005, Vol. 5745, pages 646-655, to take into account and correct the scattered radiation for a 3D reconstruction.